Thus, the process converges to a state of equilibrium fulfilling the theorem.

We know that this process has converged when the vector of influence changes only by a constant as follows.

When these two processes converge, the problem is completed.

This process of simulated evolution eventually converges towards a nearly optimal population of individuals, from the point of view of the fitness function.

The process will converge for a 2-person game if:

We also know from physics that the process eventually converges observably, no induction needed.

Indeed, since the arithmetic-geometric process converges so quickly, it provides an effective way to compute elliptic integrals via this formula.

Under mild regularity conditions this process converges on maximum likelihood (or maximum posterior) values for parameters.

Provided that this iterative process converges, the resulting fixed point will be affine invariant.

It has been shown that this process will converge (though not necessarily in a finite number of steps) towards the global solution for the overall problem.